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Mathematical Modeling and Numerical Simulation in External Flow Control

  • Conference paper
Book cover Flow Control

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 68))

Abstract

This paper presents an investigation of some active control problems for an external flow field. A series of numerical simulations are performed to investigate an unsteady viscous flow generated by a circular cylinder undergoing a combined rotary and rectilinear motion. By treating the rotation rate as a control variable, we present results of the time histories of forces acting on the cylinder surface and their time-averaged values under several types of rotations. The impact of changing rotation rate on the vortex formation, including the synchronization of cylinder and wake, is demonstrated. Based on the optimal control theory, an optimality system is formulated to determine the optimal rotation rates and the solution orbits. Though only the moving boundary mechanism is discussed, the results presented here add insight to the optimal design of control mechanism and may provide guidance to the formulation of other complex optimal flow control problems.

AMS(MOS) subject classifications. 76D05, 49120, 93C20.

This work was supported by Air Force Office of Scientific Research under AFOSR Grant F-49620-92-J-0078. The author gratefully acknowledges Professors John Burns and S.S. Sritharan for many valuable discussions on various aspects of this project. Thanks are also due to Dr. M. Coutanceau for providing the experimental results.

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Author information

Authors and Affiliations

  1. Interdisciplinary Center for Applied Mathematics, and Aerospace and Ocean Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0531, USA

    Yuh-Roung Ou

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  1. Yuh-Roung Ou
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Editors and Affiliations

  1. Department of Mathematics and Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0531, USA

    Max D. Gunzburger

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© 1995 Springer-Verlag New York, Inc.

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Ou, YR. (1995). Mathematical Modeling and Numerical Simulation in External Flow Control. In: Gunzburger, M.D. (eds) Flow Control. The IMA Volumes in Mathematics and its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2526-3_10

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  • DOI: https://doi.org/10.1007/978-1-4612-2526-3_10

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7569-5

  • Online ISBN: 978-1-4612-2526-3

  • eBook Packages: Springer Book Archive

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